Abstract
This paper proposes an invariant-set based minimal detectable fault (MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. First, a novel invariant-set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-set operations. Notably, this method does not need to satisfy the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty compared with the traditional invariant-set computation methods. Based on asymptotic stability assumptions, a family of robust positively invariant (RPI) outer-approximations of minimal robust positively invariant (mRPI) set are obtained by using a shrinking procedure. Based on the mRPI set, the healthy and faulty residual sets can be obtained. Then, by considering the dual case of the set-separation constraint regarding the healthy and faulty residual sets, we transform the guaranteed MDF problem based on the set-separation constraint into a simple linear programming (LP) problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. At the end of the paper, a practical vehicle model is used to illustrate the effectiveness of the proposed method.
Highlights
Fault diagnosis has attracted much attention from a great number of researchers owing to the demand of increasing safety and reliability of the modern industrial control systems
According to the work [17], we propose a novel and practical minimal robust positively invariant (mRPI) set computation method to characterize the healthy and faulty residual sets of perturbed discrete-time linear parameter varying (LPV) systems exclusively based on a sequence of convex-set operations without need of existence of a common quadratic Lyapunov function assumed in [16] and [14]
The mRPI set of the dynamics (5) is not a convex set [1], the robust positive invariance of the convex hull of the mRPI set for the dynamics (5) can be guaranteed by the following theorem
Summary
Fault diagnosis has attracted much attention from a great number of researchers owing to the demand of increasing safety and reliability of the modern industrial control systems. J. Tan et al.: Invariant Set-Based Analysis of MDF for Discrete-Time LPV Systems With Bounded Uncertainties the healthy and faulty residual sets are separated from each other, it is guaranteed that the occurred fault can be detected in the steady stage. According to the work [17], we propose a novel and practical mRPI set computation method to characterize the healthy and faulty residual sets of perturbed discrete-time LPV systems exclusively based on a sequence of convex-set operations without need of existence of a common quadratic Lyapunov function assumed in [16] and [14].
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